Download trigonometry (sohcahtoa)

WJEC MATHEMATICS
INTERMEDIATE
ANGLES AND GEOMETRY
TRIGONOMETRY
(SOHCAHTOA)
1
Contents
SoHCaHToA
Finding Lengths
Finding Angles
Worded Questions
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
PixiMaths
Trigonometry Exercise
2
SOHCAHTOA
The triangle above is a right angled triangle with another angle
named theta ( )
 The hypotenuse is always the side opposite the right angle
 We label the adjacent side the side that touches the angle
(That is not the hypotenuse)
 We label the opposite side the side that does not touch the
angle
From a right angled triangle labelled in this way, there are three
trigonometric ratios to learn
Often, the "cover up" method is the simplest to use.
O = opposite
S=
A = adjacent
C=
H = hypotenuse
T=
3
When answering these questions there are some steps that we do
every time.
 Step 1: Label the two sides to use (Either both known or one
known and one to find)
 Step 2: Select the triangle needed from the three seen on the
previous page
 Step 3: Cover up the letter we need to find to form an equation
 Step 4: Substitute values and solve
Finding a missing side
Example 1
Find
Step 1
Label the two sides.
The first is the hypotenuse which is
labelled and the second is the unknown
side which is adjacent to the angle
Step 2
We need to select the triangle that
contains a 'h' and an 'a'
Step 3
Cover up the letter of the unknown (a) and
form an equation
Step 4 - Substitute and solve
x
4
Example 2
Find
Step 1
Label the two sides.
The first is the side opposite to the angle
(45) and the second is the unknown side
which is adjacent to the angle
Step 2
We need to select the triangle that
contains an 'o' and an 'a'
Step 3
Cover up the letter of the unknown (a) and
form an equation
Step 4 - Substitute and solve
5
Finding a missing angle
The steps to finding a missing angle in a right angled triangle, using
SOHCAHTOA trig, are the same as finding a side length
Example
Find the size of the angle marked
Step 1
Label the two sides.
The first is the hypotenuse and the second
is the side that is opposite the angle
marked
Step 2
We need to select the triangle that
contains a 'h' and an 'o'
Step 3
Cover up the letter of the unknown and
form an equation
Step 4
Substitute the values and solve
We know the values of 'o' and 'h'
Important! We want
The inverse of
on its own!
so we cover the 's'
Remember: the 's' stands for
Type this into your calculator!
To get
press shift - sin
6
Worded / Picture Questions
Very often the question will be 'hidden' within a worded question or
picture.
Angle of elevation
The right angled triangle may be hidden in an angle of elevation
Bearings
Right angled triangles also make an appearance in Bearings
questions
7
Exercise G23
8
Exam Questions G35
1.
2.
9
3.
4.
10